{"title":"ABAQUS 中 UMAT 的 Jacobian vs. disturbance 方法:各向同性损伤力学的应用","authors":"M.R.T. Arruda , J. Shen","doi":"10.1016/j.ijnonlinmec.2024.104928","DOIUrl":null,"url":null,"abstract":"<div><div>This paper compares the computational efficiency of different methodologies to estimate the tangent stiffness applied to ABAQUS standard UMAT user-subroutine, using implicit formulation with predictor corrector methodology. It uses two new methodologies to estimate the stiffness matrix for the predictor-corrector iterative process, named Disturbance Method and Implicit to Explicit Method. With the Disturbance Method, it is enough to build UMATs using only a secant matrix, since an approximate tangential material matrix is automatically computed, promoting a faster implementation of new material constitutive relations in the ABAQUS standard. It is also studied the possibility of the use of a new algorithm that transforms the UMAT implicit formulation to an explicit formulation using a new secant predictor corrector algorithm. In this study, a new concrete damage model that considers fracture energy regularization for both tensile and compressive behaviour with Mode I Fracture is utilized. Classical and known benchmarks to test damage models in the scientific community are used to compare both methods for the calculation of the Jacobian matrix in terms of time and number of iterations.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":null,"pages":null},"PeriodicalIF":2.8000,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Jacobian vs. disturbance method for UMATs in ABAQUS: An application to isotropic damage mechanics\",\"authors\":\"M.R.T. Arruda , J. Shen\",\"doi\":\"10.1016/j.ijnonlinmec.2024.104928\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This paper compares the computational efficiency of different methodologies to estimate the tangent stiffness applied to ABAQUS standard UMAT user-subroutine, using implicit formulation with predictor corrector methodology. It uses two new methodologies to estimate the stiffness matrix for the predictor-corrector iterative process, named Disturbance Method and Implicit to Explicit Method. With the Disturbance Method, it is enough to build UMATs using only a secant matrix, since an approximate tangential material matrix is automatically computed, promoting a faster implementation of new material constitutive relations in the ABAQUS standard. It is also studied the possibility of the use of a new algorithm that transforms the UMAT implicit formulation to an explicit formulation using a new secant predictor corrector algorithm. In this study, a new concrete damage model that considers fracture energy regularization for both tensile and compressive behaviour with Mode I Fracture is utilized. Classical and known benchmarks to test damage models in the scientific community are used to compare both methods for the calculation of the Jacobian matrix in terms of time and number of iterations.</div></div>\",\"PeriodicalId\":50303,\"journal\":{\"name\":\"International Journal of Non-Linear Mechanics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2024-10-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Non-Linear Mechanics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0020746224002932\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Non-Linear Mechanics","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020746224002932","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
摘要
本文比较了应用于 ABAQUS 标准 UMAT 用户子程序的不同方法估算切线刚度的计算效率,使用的是隐式表述与预测器校正器方法。它使用两种新方法来估算预测器-校正器迭代过程的刚度矩阵,分别称为 "扰动法 "和 "隐式转显式法"。使用扰动法时,只需使用正割矩阵即可建立 UMAT,因为会自动计算近似切向材料矩阵,从而促进在 ABAQUS 标准中更快地实施新的材料构成关系。此外,还研究了使用新算法的可能性,该算法利用新的等值线预测校正器算法将 UMAT 隐式公式转换为显式公式。在这项研究中,使用了一种新的混凝土损伤模型,该模型考虑了具有模式 I 断裂的拉伸和压缩行为的断裂能量正则化。利用科学界测试破坏模型的经典和已知基准,从时间和迭代次数的角度对这两种计算雅各矩阵的方法进行了比较。
Jacobian vs. disturbance method for UMATs in ABAQUS: An application to isotropic damage mechanics
This paper compares the computational efficiency of different methodologies to estimate the tangent stiffness applied to ABAQUS standard UMAT user-subroutine, using implicit formulation with predictor corrector methodology. It uses two new methodologies to estimate the stiffness matrix for the predictor-corrector iterative process, named Disturbance Method and Implicit to Explicit Method. With the Disturbance Method, it is enough to build UMATs using only a secant matrix, since an approximate tangential material matrix is automatically computed, promoting a faster implementation of new material constitutive relations in the ABAQUS standard. It is also studied the possibility of the use of a new algorithm that transforms the UMAT implicit formulation to an explicit formulation using a new secant predictor corrector algorithm. In this study, a new concrete damage model that considers fracture energy regularization for both tensile and compressive behaviour with Mode I Fracture is utilized. Classical and known benchmarks to test damage models in the scientific community are used to compare both methods for the calculation of the Jacobian matrix in terms of time and number of iterations.
期刊介绍:
The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear.
The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas.
Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.